Domain palenty

How to check if my domain has got any palenty ? also how to remove no follow links I purcahsed frorm third party for my website.

To remove links you need to submit a disavow request to Google.

Use GSC for manual actions Ahrefs or SEMrush for algorithmic penalties. For nofollow links, reach out to the seller. If no response, disavow in GSC to be safe.

ShadowScavenger said:

How to check if my domain has got any palenty ?

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to expand on @NeedMyLink 's great advice....

If you add your domain to GSC sometimes you can see the manual penalties in there. If no manual penalty shows up it's still possible for the domain to be manually penalized but you not knowing. But this is the closest thing we have to seeing manual penalties, so add it to your GSC and check for the penalty...

For algorithmic penalties any decent SEO tool can show you this. Just look at the traffic / rankings graphs, and if you see sudden drops it's 100% penalized, if there are no sudden drops but gradual ones over many months (3-12 for example) it could either be penalty, or loss of rankings due to competition taking over your spots. So this one is a bit harder to asses, but it's still possible to be a penalty if the drops are gradual instead of sudden.

ShadowScavenger said:

also how to remove no follow links I purcahsed frorm third party for my website.

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just contact the guys that you purchased them from and tell them "hey, man! I don't need the links anymore, can you please remove them".

Although, I don't know why you'd want to do this. If the links are good and / or don't harm your site you should keep them even if they're nofollow.

Contact the webmasters and get help to remove those or use the Google's disavow tool